TY - JOUR
T1 - A universal space for plus-constructions
AU - Berrick, A. J.
AU - Casacuberta, Carles
PY - 1999/1/1
Y1 - 1999/1/1
N2 - We exhibit a two-dimensional, acyclic, Eilenberg-Mac Lane space W such that, for every space X, the plus-construction X+ with respect to the largest perfect subgroup of π1(X) coincides, up to homotopy, with the W-nullification of X; that is, the natural map X → X+ is homotopy initial among maps X → Y where the based mapping space map*(W, Y) is weakly contractible. Furthermore, we describe the effect of W -nullification for any acyclic W, and show that some of its properties imply, in their turn, the acyclicity of W. © 1999 Elsevier Science Ltd. All rights reserved.
AB - We exhibit a two-dimensional, acyclic, Eilenberg-Mac Lane space W such that, for every space X, the plus-construction X+ with respect to the largest perfect subgroup of π1(X) coincides, up to homotopy, with the W-nullification of X; that is, the natural map X → X+ is homotopy initial among maps X → Y where the based mapping space map*(W, Y) is weakly contractible. Furthermore, we describe the effect of W -nullification for any acyclic W, and show that some of its properties imply, in their turn, the acyclicity of W. © 1999 Elsevier Science Ltd. All rights reserved.
UR - https://www.scopus.com/pages/publications/0033130276
U2 - 10.1016/S0040-9383(97)00073-6
DO - 10.1016/S0040-9383(97)00073-6
M3 - Article
SN - 0040-9383
VL - 38
SP - 467
EP - 477
JO - Topology
JF - Topology
IS - 3
ER -